Question

Trigonometric identities assignment 4

Simplify 5 sin ø sec ø

A. 5 cot ø
B. 5
C. 5 cos ø
D. 5 tan ø

Answer 1

D. 5 tan ø

Explanation:

`5 \sin \phi \: \sec \phi \\ \\ = 5 \sin \phi \: * (1)/( \cos \phi) \\ \\ = 5 (\sin \phi)/( \cos \phi) \\ \\ = 5 \tan \phi`

Answer 2

Correct choice D.

Explanation:

Trigonometric Identities

We need to recall some properties and definitions of the trigonometric functions.

`\tan \theta=(\sin\theta)/(\cos\theta)`

`\sec \theta=(1)/(\cos\theta)`

It's required to simplify the following expression:

`5\sin\theta\sec\theta`

Substituting the identity for the secant:

`\displaystyle 5\sin\theta\sec\theta=5\sin\theta.(1)/(\cos\theta)`

Operating:

`\displaystyle 5\sin\theta\sec\theta=5(\sin\theta)/(\cos\theta)`

Now we use the definition of the tangent:

`\displaystyle 5\sin\theta\sec\theta=5\tan\theta`

Correct choice D.